Well, the game unfortunately doesn't give much info on the war, so unless it was elaborated better in the comics or novels, the truth can only be speculated...
Anyway:
Only two things here: the Republic may have had the advantage in numbers and supplies, but the Mandalorians were a warrior race, with superior training, motivation and probably technology. So either the all Republic commanders were the biggest idiots in the galaxy, or the Republic Fleet wasn't too advantaged. Also, the jedi went to war with Revan, not before him.
Revan himself was was still only a knight, charismatic as you want, but that sure couldn't grant him the command of the entire Fleet. Then his forces were limited in numbers, and probably weren't more than the mandalorian's legions.
At this point, he managed not only to hold them off, but force them to retreat. With the limitations above, he might have done something good with them after all... "
Maybe, maybe not. That's speculation too.